HiFi Loudspeaker Design

Acoustics

Basics

When vibration sound disturbs particles in the air or the other medium,
then those particles displace other surrounding particles.
This particle movement goes on continuously in the outward direction to form a wave
pattern.
The wave carries the sound energy through the medium and becomes less intense as it
moves
away from the source. The sound energy is also directly associated with the volume of
the sound.
Higher sound energy results in loud volume.
There are three aspects of a sound wave that cause different types of sounds to be
produced:
frequency, wavelength and amplitude. Sound waves vibrate at different rates or
frequencies as
they move through the medium. The wave may have a single frequency or many frequencies
depending
upon the vibration source.
Let us consider a sound wave of constant frequency generated by a source with
displacement
function on Y-axis and time function on X-axis (Fig. 1). The number of waves generated
per second
is the frequency of the sound and expressed in hertz (Hz). The maximum displacement of a
peak is
termed as amplitude while the distance from one peak to the other is the wavelength. The
sinusoidal
wave gen- erates only single frequency. A variety of non-repetitive sounds produce waves
of different
frequencies.

Fig. 1

Absorption and diffusion

Music is often performed in reverberant spaces; spaces were the sound
bounces around many times before slowly dying away. Whether auditoriums,
concert halls or stadiums, these spaces are intentionally designed to have
lots of reflective surfaces. The best concert hall can have surprisingly
little absorptive material. But your living room needs more. Its dimensions
are smaller and so reverberation does not add the great sonic character of
Boston Symphony Hall, it just adds sonic muddle. Besides, the recording that
you paid good money for already has the sonic footprint of that large
carefully designed performance space. Your living room does not need to add
its footprint on top of that. In truth, your living room needs to absorb as
much sound as possible. It needs to be acoustically dead.

A good room generally has a "quietness" to it. Your can carry on a soft
conversation and fully understand the person you are talking to. Street
noise may make it in to the room but it is well damped and unobtrusive. This
quality of quietness comes from having a good percentage of all surfaces
covered with acoustically absorptive materials. These can be heavy drapes,
thick carpets, stuffed pieces of furniture, etc. Openings to the rest of the
house absorb sound too, because they let it escape down the hall where it is
more likely to be absorbed than reflected back to you.

Different than absorption, but equally desirable, is the scattering of
sound. A large flat surface bounces sound waves back as an undisturbed
front. These large reflections may be heard as an echo, at the very least
they up the sonic harshness, degrade stereo clarity and upset the balance of
sound. Anything that breaks up the surface will take that sonic wave and
scatter it in multiple directions. Not only does that reduce the severity of
reflections, it tends to promote energy loss by giving the sound a longer
path (hence more chances to hit an absorptive area) before it gets back to
your ears, all good stuff.

So the two main components determining room acoustics are
absorption
and diffusion.

Make a mental tally of what percentage of the rooms surfaces are hard and
flat, what percentage have scattering surface irregularities.

Front wall has drapes by windows (good)

Drapes are open revealing a lot of glass (bad)

Nothing but sheetrock on that ceiling (bad)

Thick carpet on the floor, with under padding (very good)

Large sofa in front of side wall (good)

By now you should be starting to get a sense of what good and bad sounding
rooms consist of. If you want a great example of a bad sounding room, pick
up any architectural magazine. See that designer-look room with hardwood
floors and nary a throw rug, minimalist furniture, expansive glass walls
(nice view) and clean uncluttered walls? Bad acoustics, I guarantee it.

So what can we do with our room to improve its acoustics, short of bringing
in the wrecking crew and starting over?

Add absorption. As a rule of thumb, try to cover 1/3rd of all
surfaces with something soft. Purpose built audio absorbers are
available but are frequently ugly and not the only solution. A large empty
wall can have a rug hung on it. I knew a person that collected oriental
rugs. They did not want to walk on the silk rugs in their collection so they
hung a few on the walls. (Hint: hide a layer of carpet backing behind it to
further increase its absorptive properties.) At least put a large area rug
over the center of that hardwood floor. Put a thick pad underneath it.
Drapes for the windows add a lot of absorption, especially if they are heavy
or thickly lined.

Add diffusion. Again, commercial solutions are available but there are many
domestic solutions. One of the best diffusers of sound is a bookcase half
full of books. Some three dimensional art objects can diffuse sound.
Decorative room dividers (the zigzag kind) can absorb or diffuse sound.
Anything that breaks up that big expanse of hard plaster or drywall will
help diffuse sound.

The drawing below shows the path of the primary bounces of sound in a
typical rectangular room. Although placing these absorptive and diffusive
sound objects anywhere in the room will have some effect, you can maximize
the effect by placing them directly in the path of these primary sonic
paths. This guarantees that strong hard reflections are scattered or
absorbed. These early reflections are especially dangerous to the clarity of
sound and to the stereo effect. Absorbing or scattering them will up the
clarity of movies or music.

Sound waves are principally longitudinal waves. It means the wave medium, for instance,
air,
oscillates parallel to the wave’s direction. Let us consider a soft coil is stretched
and fixed
at one end. If the coil is quickly pushed and pulled from the other end, it will
compress and
elongate along with the force direction. The same thing happens in longitudinal sound
wave.
Air particles get oscillated back and forth in the direction parallel to the sound wave
movement.
This create compression and rar- efaction waves alternately. Longitudinal waves begin
with compression
followed by rarefaction. The wavelength can be determined by measuring the distance
between two
consecutive compressions, or rarefactions.

The sound wave interact with the material or object surface and may be absorbed,
transmitted,
reflected, refracted or diffracted form the surface depending on type of the surface.
These phenomenons are described in Fig. 3. When all the emitted sound waves are absorbed
by the
receiver, sound absorption occurs. It is exactly like sponge absorbing water. Sound
absorption
is an important phenomenon as far as sound insulation is concerned. There are different
materials
available for sound absorption. The sound absorbers may be porous or resonant type.
Porous absorbents
are classified as fibrous materials and open-celled foams. Fibrous materials convert
acoustic energy
into heat energy when sound waves impinge the absorber. In case of foam, sound wave
displacement
occurs through a narrow passage of foam and causes heat loss. Resonance absorbents are
of
mechanical type, where there is a solid plate with a tight air space behind. It is
noteworthy that
some material such as foam absorbs sound waves whereas the glass blocks it. The
selection of material
to be used depends on the end use application. For example, the office room in a
building can be designed
as sound absorbing or sound proofing.

Fig. 2

Sound absorption measures the amount of energy absorbed by the material and expressed as
sound absorption
coefficient (α). The coefficient ranges between 0 and 1 where 0 is no absorption and 1
is highest or
total absorption. The higher coef- ficient yields lower reverberation time. The
reverberation time is
persistence of sound in a space after a sound source has been stopped. It is the time
lag,
in seconds, for the sound to decay by 60 dB after a sound source has been stopped. Sound
absorption
is important to make the acoustic environment suitable for a specific purpose; for
instance, in
recording studios, lecture halls, concert rooms, lecture theatres, etc. The low
frequency sound
of 500 Hz is relatively difficult to absorb than high frequency sound.

Reflection

When sound waves impinge on hard or smooth surface they may reflect back with their full
energy without
altering their characteristics. The reflection angle of sound wave from the reflecting
surface is equal
to the angle of incidence. The angles are defined between a normal to the reflecting
plane and the incident
and reflected waves. The reflected sound waves, thus, follow Huygen’s geometry where
both the incidence and
reflection angles are equal.
The reflection phenomenon of sound waves finds many applications. For example, a
reflected sound wave is
used to measure the depth of water from sea level with the help of echo produced from
the reflective surface.
The geological composition at the bottom of the ocean and inside the earth crust is also
identified
using the reflection of sound wave. Echo is a simple example of sound reflection
phenomenon.
Echo can be heard when the sound wave, perpendicular to the sound source, hits a flat
and smooth surface.

Diffraction

Diffraction involves a change in the direction of sound waves as it strikes through a
surface.
Sound waves when impact on a partial barrier, some of them get reflected, some propagate
without any
disturbance and some bent or diffract over the top of the barrier. As sound source moves
closer to
the barrier, less sound diffraction is obtained. The sound at lower frequencies tends to
diffract more
easily than sound at higher frequencies

Critical Distance

Critical Distance is where the direct and reverberant sound
energies
are equal. Critical Distance is different at all frequencies. The more
reverberant a room, the closer is Critical Distance. The more absorbent a
room, the further is Critical Distance. (Critical Distance is
different
at all frequencies).

For good acoustic design the Critical Distance should be as far as possible
from the sound source, and the resultant reverberation minimal and even at
all frequencies. Direct sound from the speaker system diminishes in level,
as a function of the distance (inverse square law) whereas reverberation
constantly spreads throughout the room. Because there is new incoming sound
from the speakers, reverberation keeps building up, until the new incoming
sound, equals the sound absorbed (steady-state).

When the reverberant sound becomes 12db or greater than the direct sound all
intelligibility is lost. The simplest way to find 'Critical Distance' is to
play compressed pop music through the sound system.
Begin with one speaker (left or right). Walk back and forth around the room,
and you will be surprised how easy it is to identify the critical distance.
Repeat the exercise with the other speaker, then both speakers.
Its surprising how accurate our ears are, when compared with acoustic
measurement microphones.

The more reverberant the room is the closer the Critical Distance.

The more absorbent the room is the further the Critical Distance.

Near field or Direct field is inside the Critical Distance.

Far field or Reverberant field is outside the Critical Distance.

Sound Pressure Level

Sound pressure level is a measure of volume (loudness) of the sound in terms of the
sound pressure.
The level can be determined by measuring the sound pressure disturbance from the
equilibrium pressure value.
The pressure disturbance is the difference between the instantaneous pressure and the
static pressure.
The mean pressure deviation from the equilibrium is always zero, since the mean
compression waves are equal
to mean rarefaction waves. These positive and neg- ative effects are converted into
positive using the root
mean square (RMS) value of sound pressure (Prms) over a period of time. However, RMS
value of sound pres- sure
is not convenient to use as it varies over a wide range of magnitudes.
The decibel (dB) is the easiest and a more convenient way to measure the volume
(loudness) of the sound in
terms of the sound pressure.

dB = Sound pressure level

rms = Root mean square value

po = Reference pressure

Decibel is a value on a logarithmic scale and it is based on the capacity of
humans to sense sound pressure. Sound perception by humans is subjective in nature.
Different exposure times
of the same sound pressure may have different effects on hearing. In general, it is
recommended that
sound pressure levels should not exceed 30 and 40 dB in resting room and kitchen.
The sound pressure level beyond 90 dB may be harmful for human hearing, especially when
the exposure time is high.